Nonbinary refers to any gender that is not exclusively male or female. A similar term is genderqueer.
Some common nonbinary gender identities include: agender, bigender, genderfluid, androgyne, and neutrois.
It is usually considered to be under the transgender umbrella, and some nonbinary people will also identify as trans.

Fallon: You're not a girl or a boy, are you?
Skylar: Nope, I'm not! I'm nonbinary.

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Usually under the genderqueer or transgender umbrellas. when someone's sense of gender is not male, female, or something in-between (androgynous). Includes neutrois, agender, genderless, gender-neutral, and other senses of gender devoid of male or female aspects.

They don't identify themself as male nor female, perhaps they are non-binary?

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Not unlike "gender fluid," non-binary is a term made up by angry youngsters who are yearning to be part of a culture of victimization and enjoy jerking one another off by romanticizing mental illness on tumblr.